1. Factoring Part 3

2. FACTORING #1: Take out the GCFEX: 2x 4 – 8x 3 + 4x 2 – 6x How to do it…. Find what is in common in each term and put in front. See what is left over. Check answer by distributing. Solution:

3. FACTORING #1: Take out the GCFEX: 2x 4 – 8x 3 + 4x 2 – 6x How to do it…. Find what is in common in each term and put in front. See what is left over. Check answer by distributing. Solution: 2x( )

4. FACTORING #1: Take out the GCFEX: 2x 4 – 8x 3 + 4x 2 – 6x How to do it…. Find what is in common in each term and put in front. See what is left over. Check answer by distributing. Solution: 2x(x 3 )

5. FACTORING #1: Take out the GCFEX: 2x 4 – 8x 3 + 4x 2 – 6x How to do it…. Find what is in common in each term and put in front. See what is left over. Check answer by distributing. Solution: 2x(x 3 – 4x 2 )

6. FACTORING #1: Take out the GCFEX: 2x 4 – 8x 3 + 4x 2 – 6x How to do it…. Find what is in common in each term and put in front. See what is left over. Check answer by distributing. Solution: 2x(x 3 – 4x 2 + 2x )

7. FACTORING #1: Take out the GCFEX: 2x 4 – 8x 3 + 4x 2 – 6x How to do it…. Find what is in common in each term and put in front. See what is left over. Check answer by distributing. Solution: 2x(x 3 – 4x 2 + 2x – 3)

8. FACTORING #1: Take out the GCFEX: 15xy 2 – 10x 3 y + 25xy 3 How to do it…. Find what is in common in each term and put in front. See what is left over. Check answer by distributing out. Solution:

9. FACTORING #1: Take out the GCFEX: 15xy 2 – 10x 3 y + 25xy 3 How to do it…. Find what is in common in each term and put in front. See what is left over. Check answer by distributing out. Solution: 5xy( )

10. FACTORING #1: Take out the GCFEX: 15xy 2 – 10x 3 y + 25xy 3 How to do it…. Find what is in common in each term and put in front. See what is left over. Check answer by distributing out. Solution: 5xy(3y )

11. FACTORING #1: Take out the GCFEX: 15xy 2 – 10x 3 y + 25xy 3 How to do it…. Find what is in common in each term and put in front. See what is left over. Check answer by distributing out. Solution: 5xy(3y – 2x 2 )

12. FACTORING #1: Take out the GCFEX: 15xy 2 – 10x 3 y + 25xy 3 How to do it…. Find what is in common in each term and put in front. See what is left over. Check answer by distributing out. Solution: 5xy(3y – 2x 2 + 5y 2 )

13. FACTORING #2: Trinomials with a leading coefficient of 1. EX: x 2 + 5x + 6 How to do it…. Make a table of factors of the last number. Pick the factors that add up to the middle number. Solution:

14. FACTORING #2: Trinomials with a leading coefficient of 1. EX: x 2 + 5x + 6 How to do it…. Make a table of factors of the last number. 6 1 6 2 3 Pick the factors that add up to the middle number. Solution:

15. FACTORING #2: Trinomials with a leading coefficient of 1. EX: x 2 + 5x + 6 How to do it…. Make a table of factors of the last number. 6 1 6 2 3 Pick the factors that add up to the middle number. Solution:

16. FACTORING #2: Trinomials with a leading coefficient of 1. EX: x 2 + 5x + 6 How to do it…. Make a table of factors of the last number. 6 1 6 2 3 Pick the factors that add up to the middle number. Solution: (x + 2)(x + 3)

17. FACTORING #2: Trinomials with a leading coefficient of 1. EX: x 2 + 5x + 6 How to do it…. Make a table of factors of the last number. 6 1 6 2 3 Pick the factors that add up to the middle number. Solution: (x + 2)(x + 3) Check with FOIL

18. FACTORING #2: Trinomials with a leading coefficient of 1. EX: x 2 + 7x + 12 How to do it…. Make a table of factors of the last number. Pick the factors that add up to the middle number. Solution:

19. FACTORING #2: Trinomials with a leading coefficient of 1. EX: x 2 + 7x + 12 How to do it…. Make a table of factors of the last number. 12 1 12 2 6 3 4 Pick the factors that add up to the middle number. Solution:

20. FACTORING #2: Trinomials with a leading coefficient of 1. EX: x 2 + 7x + 12 How to do it…. Make a table of factors of the last number. 12 1 12 2 6 3 4 Pick the factors that add up to the middle number. Solution:

21. FACTORING #2: Trinomials with a leading coefficient of 1. EX: x 2 + 7x + 12 How to do it…. Make a table of factors of the last number. 12 1 12 2 6 3 4 Pick the factors that add up to the middle number. Solution: (x + 3)(x + 4)

22. FACTORING #2: Trinomials with a leading coefficient of 1. EX: x 2 + 7x + 12 How to do it…. Make a table of factors of the last number. 12 1 12 2 6 3 4 Pick the factors that add up to the middle number. Solution: (x + 3)(x + 4) Check with FOIL.

23. FACTORING #2: Trinomials with a leading coefficient of 1. EX: x 2 + 7x + 6 How to do it…. Make a table of factors of the last number. Pick the factors that add up to the middle number. Solution:

24. FACTORING #2: Trinomials with a leading coefficient of 1. EX: x 2 + 7x + 6 How to do it…. Make a table of factors of the last number. 6 1 6 2 3 Pick the factors that add up to the middle number. Solution:

25. FACTORING #2: Trinomials with a leading coefficient of 1. EX: x 2 + 7x + 6 How to do it…. Make a table of factors of the last number. 6 1 6 2 3 Pick the factors that add up to the middle number. Solution:

26. FACTORING #2: Trinomials with a leading coefficient of 1. EX: x 2 + 7x + 6 How to do it…. Make a table of factors of the last number. 6 1 6 2 3 Pick the factors that add up to the middle number. Solution: (x + 6)(x + 1)

27. FACTORING #2: Trinomials with a leading coefficient of 1. EX: x 2 + 7x + 6 How to do it…. Make a table of factors of the last number. 6 1 6 2 3 Pick the factors that add up to the middle number. Solution: (x + 6)(x + 1) Check with FOIL.

28. FACTORING #2: Trinomials with a leading coefficient of 1. EX: notice the signs x 2 - 5x + 4 How to do it…. Make a table of factors of the last number. Pick the factors that add up to the middle number. Solution:

29. FACTORING #2: Trinomials with a leading coefficient of 1. EX: notice the signs x 2 - 5x + 4 How to do it…. Make a table of factors of the last number. 4 1 4 2 2 Pick the factors that add up to the middle number. Solution:

30. FACTORING #2: Trinomials with a leading coefficient of 1. EX: notice the signs x 2 - 5x + 4 How to do it…. Make a table of factors of the last number. 4 1 4 2 2 Pick the factors that add up to the middle number. None of these work! Solution:

31. FACTORING #2: Trinomials with a leading coefficient of 1. EX: notice the signs x 2 - 5x + 4 How to do it…. Make a table of factors of the last number. 4 1 4 2 2 Pick the factors that add up to the middle number. None of these work! TRY negatives Solution:

32. FACTORING #2: Trinomials with a leading coefficient of 1. EX: notice the signs x 2 - 5x + 4 How to do it…. Make a table of factors of the last number. 4 -1 -4 -2 -2 Pick the factors that add up to the middle number. None of these work! TRY negatives Solution:

33. FACTORING #2: Trinomials with a leading coefficient of 1. EX: notice the signs x 2 - 5x + 4 How to do it…. Make a table of factors of the last number. 4 -1 -4 -2 -2 Pick the factors that add up to the middle number. None of these work! TRY negatives Solution:

34. FACTORING #2: Trinomials with a leading coefficient of 1. EX: notice the signs x 2 - 5x + 4 How to do it…. Make a table of factors of the last number. 4 -1 -4 -2 -2 Pick the factors that add up to the middle number. None of these work! TRY negatives Solution: (x – 1)(x – 4)

35. FACTORING #2: Trinomials with a leading coefficient of 1. EX: notice the signs x 2 - 5x + 4 How to do it…. Make a table of factors of the last number. 4 -1 -4 -2 -2 Pick the factors that add up to the middle number. None of these work! TRY negatives Solution: (x – 1)(x – 4) Check with FOIL.

36. x 2 + 6x + 5 =

37. x 2 + 6x + 5 = (x + 5)(x + 1)

38. x 2 + 10x + 16 =

39. x 2 + 10x + 16 = (x + 2)(x + 8)

40. a 2 – 5a + 6 =

41. a 2 – 5a + 6 = (a – 2)(a – 3)

42. #2: Trinomials with a leading coefficient of 1. EX: notice the signs x 2 + 2x - 15 How to do it…. Make a table of factors of the last number. Pick the numbers that add to be the middle number. Solution:

43. #2: Trinomials with a leading coefficient of 1. EX: notice the signs x 2 + 2x - 15 How to do it…. Make a table of factors of the last number. 15 1 -15 3 -5 -1 15 -3 5 Pick the numbers that add up to be the middle number. Solution:

44. #2: Trinomials with a leading coefficient of 1. EX: notice the signs x 2 + 2x - 15 How to do it…. Make a table of factors of the last number. 15 1 -15 3 -5 -1 15 -3 5 Pick the numbers that add up to be the middle number. Solution:

45. #2: Trinomials with a leading coefficient of 1. EX: notice the signs x 2 + 2x - 15 How to do it…. Make a table of factors of the last number. 15 1 -15 3 -5 -1 15 -3 5 Pick the numbers that add up to be the middle number. Solution: (x + 5)(x – 3)

46. #2: Trinomials with a leading coefficient of 1. EX: notice the signs x 2 + 2x - 15 How to do it…. Make a table of factors of the last number. 15 1 -15 3 -5 -1 15 -3 5 Pick the numbers that add up to be the middle number. Solution: (x + 5)(x – 3) Check with FOIL.

47. y 2 + 3y - 10 =

48. 10

49. y 2 + 3y - 10 = 10 1 -10 2 -5 -1 10 -2 5

50. y 2 + 3y - 10 = 10 1 -10 2 -5 -1 10 -2 5

51. y 2 + 3y - 10 = 10 1 -10 2 -5 -1 10 -2 5 (x + 5)(x – 2)